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Difference between revisions of "2007 AMC 12B Problems/Problem 1"

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==Solution==
 
==Solution==
  
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There are four walls in each bedroom, since she can't paint floors or ceilings. So we calculate the number of square feet of wall there is in one bedroom:
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There are four walls in each bedroom (she can't paint floors or ceilings). Therefore, we calculate the number of square feet of walls there is in one bedroom:
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<cmath>(12*8)+(12*8)+(10*8)+(10*8)-60=160+192-60=292</cmath>
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<cmath>2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292</cmath>
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We have three bedrooms, so she must paint <cmath>292*3=876 \Rightarrow \fbox{(E)}</cmath> square feet of walls.
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We have three bedrooms, so she must paint <math>292\cdot3=\boxed{\textbf{(E) }876}</math> square feet of walls.
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~MathFun1000
  
 
==See Also==
 
==See Also==

Latest revision as of 09:19, 7 March 2022

The following problem is from both the 2007 AMC 12B #1 and 2007 AMC 10B #1, so both problems redirect to this page.

Problem

Isabella's house has $3$ bedrooms. Each bedroom is $12$ feet long, $10$ feet wide, and $8$ feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy $60$ square feet in each bedroom. How many square feet of walls must be painted?

$\mathrm{(A)}\ 678 \qquad \mathrm{(B)}\ 768 \qquad \mathrm{(C)}\ 786 \qquad \mathrm{(D)}\ 867 \qquad \mathrm{(E)}\ 876$

Solution

There are four walls in each bedroom (she can't paint floors or ceilings). Therefore, we calculate the number of square feet of walls there is in one bedroom: \[2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292\] We have three bedrooms, so she must paint $292\cdot3=\boxed{\textbf{(E) }876}$ square feet of walls.

~MathFun1000

See Also

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by
First question 		Followed by
Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions
2007 AMC 10B (Problems • Answer Key • Resources)
Preceded by
First Problem 		Followed by
Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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